This circuit diagram shows the wiring for a new receptacle outlet connected at a light fixture. The source at the fixture is always hot and a switch loop controls the light. New 2-wire cable runs from the fixture box to the new receptacle and the source hot, neutral, and ground are splice to it along with a pigtail back to the fixture circuit. With this arrangement the new receptacle is always hot.
Back at the source, the white neutral wire is spliced to the white from the fixture cable and to a pigtail, back to the receptacle neutral terminal. At the fixture the white connects to the neutral terminal on the light. The hot terminal on the light is connected to the red wire from the switch loop cable and the other end is connected to the top terminal on the switch.
This diagram is similar to the one above, but the switch comes before the new light in the circuit. New cable is run from the receptacle to the new switch location and from there to the light location. The switch may also be added in the the same box with the receptacle as in the diagrams at this link, where the two are installed in a double-gang electrical box.
At the switch, the other end of the black wire is connected to the bottom terminal on the switch and the black wire going to the new light is connected to the top terminal. The white wire from the receptacle is spliced to the white wire going to the light, it doesn’t connect to the switch in this diagram, but a new electronic switch will usually include a neutral wire connection. At the light the black wire connects to the hot terminal on the fixture and the white goes to the neutral terminal.